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Stabilizer Formalism

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Admin

  • Pset5 is 30% of your grade, and consists of:

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    • Part 1: 4 Problems, including running circuits on IBM’s quantum machines
    • Due December 11, 11:59pm

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    • Part 2: Designing a bot to play Qubit Tug-of-War (details this Wednesday)
    • Due December 14, 11:59pm.

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  • Remember to add your IBM Quantum Login to the spreadsheet (see EdStem post #191)

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Stabilizer formalism

Last time we were introduced to quantum error correction.

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Saw 9-qubit Shor code, heard about 7-qubit and 5-qubit codes, as well as about the Toric Code (also known as Surface Code).

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These codes can get rather complicated, but can be neatly described and analyzed using Stabilizer Formalism. These codes are also called Stabilizer Codes.

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Stabilizer formalism is important beyond error correcting codes: it shows up everywhere in quantum computation and quantum information.

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Stabilizer gates and circuits

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Stabilizer gates and circuits

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Stabilizer gates and circuits

Although not universal, stabilizer circuits show up in many places:

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  • Encoding/decoding/correction of Shor’s 9-qubit code

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Stabilizer states

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Stabilizer states

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Stabilizer states

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Math aside

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Stabilizer states

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Pauli matrices

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Pauli matrices

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Pauli matrices

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Stabilizer group

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Stabilizer groups

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Stabilizer groups

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Stabilizer states

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Stabilizer group generators

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Reasoning about stabilizer states

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Reasoning about stabilizer states

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Reasoning about stabilizer states

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Reasoning about stabilizer states

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